The Grammar of Statements of Natural Laws

There seem to be two main characteristics of the logic of law statements. First they are supposed to cover every case in a certain domain of phenomena. Let us refer to this as the universal scope of the law. When exceptions turn up there are strategies for preserving the law by restructuring the domain to which it is germane. Laws are presumed to be conjoined with tacit ceteris paribus conditions. Second, natural law statements are supposed to express a necessity; that which a law of nature expresses could not have been otherwise. Let us refer to this feature as the modality of the law.Universality is qualified in practice. The law statement might be meant to cover the behaviour of all instances of a certain substance, say water; it might be meant to cover the behaviour of all substances of a certain kind, say all liquids; it might be meant to cover the behaviour of all material stuffs in general, all liquids, solids and gases, whether elemental or compound. There is a time restriction on the use of the last of these levels of generality, namely that the law cannot be applied too near to the big bang when there were no atoms and molecules as we know them, and so no chemical processes. Perhaps we should also restrict the application of chemical laws to times not too close to the final state of the universe when such atoms and molecules as there are will be too far apart to interact as the expansion of space-time passes a certain threshold.Modality as necessity can usefully be captured in the intuition that the statement in question cannot intelligibly be negated. This intuition can reflect two very different kinds of beliefs or presumptions as to what the function of the law statement could be. It may be that those who hold to the law believe that there is a stable natural mechanism that accounts for the regularity covered by it, as a matter of empirical fact. However, some universal statements are taken to be necessary because their function is not to describe the ways things must be with a pre-given vocabulary, but rather to express a rule which fixes some aspect of the meaning of the descriptive terms that appear in the ‘law’. It may be that the law only seems to be about material stuff in the material world. It expresses a semantic rule rather than a putative matter of fact. Newton's Second Law, that the force acting on a body is the product of mass and acceleration, has sometimes been treated as a definition of ‘force’ as that which produces acceleration. Frederick Waismann once declared2 that all statements ever uttered by chemists, except the most recent, were necessary truths, since they served to amplify the criteria of identity for the substances in question.2Personal communication.A useful supplement to the category of laws in the strict sense comes from the writings of Nelson Goodman [1983]. Scientific discourse is full of modally qualified general statements that have something of the character of exemplary laws such as Newton's Laws of Motion. He suggests widening the category of statements that are general in scope and modally necessary to include ‘law-like’ statements. A closely related concept is that of nomologicality. A nomological statement is one which has the character of a law, that is general in scope and is treated as having some degree of necessity.